EXISTENCE RESULT FOR A CLASS OF N-LAPLACIAN EQUATIONS INVOLVING CRITICAL GROWTH

被引：0

作者：

章国庆 ^{[1
]}

张卫国 ^{[1
]}

刘三阳 ^{[2
]}

机构：

[1] College of Sciences, University of Shanghai for Science and Technology

[2] College of Mathematics and Statistics, Xidian

来源：

Acta Mathematica Scientia(English Series) | 2017年 / 37卷 / 05期

关键词：

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this paper, we consider a class of N-Laplacian equations involving critical growth{-?N u = λ|u|N-2 u + f（x, u）, x ∈ ?,u ∈ W01,N（?）, u（x） ≥ 0, x ∈ ?,where ? is a bounded domain with smooth boundary in RN（N > 2）, f（x, u） is of critical growth. Based on the Trudinger-Moser inequality and a nonstandard linking theorem introduced by Degiovanni and Lancelotti, we prove the existence of a nontrivial solution for any λ > λ1, λ = λ?（? = 2, 3, ···）, and λ? is the eigenvalues of the operator(-?N, W01,N（?）),which is defined by the Z2-cohomological index.

引用

页码：1348 / 1360

页数：13

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